Simulation of torsion relaxation auto-oscillations of drill string bit with viscous and Coulombic friction moment models

Abstract

The non-linear wave model of torsion pendulum is elaborated with the aim to simulate bifurcations of auto-oscillations of superdeep drill strings (DSs). The constitutive differential equation with delay argument and small parameter before the superior derivative is deduced. The results of its analysis testify that the self-excited torsional oscillations of the DS are of the relaxation type with fast and slow motions and proceed in the manner of quantized time. In doing so, the rotation speed φ changes by portions and continues to be constant during time segments Δτ, which equaled the duration of the torsion wave up and down propagation through the DS length.

The states of limit cycle birth and loss in superdeep DSs are found, and the DS torsion modes are constructed for the critical situations. The dependence of the auto-oscillation generation states on the friction (cutting) moment parameters is analysed.